Arithmetic and Geometric Progressions

You are here: Home  CAT Questionbank   CAT Quant  AP, GP  Question 7

Arithmetic Progression

    If 4 times the 4th term of an A.P. is equal to 9 times the 9th term of the A.P., what is 13 times the 13th term of this A.P.?
    1. 7 times the 13th term
    2. 0
    3. 13 times the 7th term
    4. 4 times the 4th term + 9 times the 9th term


  • Correct Answer
    Choice B. 0

Explanatory Answer

Click to watch video solution
Click to view the explanation as a slide show

Detailed Solution

4t 4 = 9t 9 , we need to find t13

4(a + 3d) = 9(a + 8d)

4a + 12d = 9a + 72d

=> 5a + 60d = 0

=> a + 12d = 0

=> t13 = 0

=> 13 × t"13" = 0

As a simple rule, if n × tn = m × tm, then tm+n = 0. See, if you can prove this.

Answer choice (b).

Correct Answer: 0

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play

More questions from Progressions

  1. Counting and Progressions
  2. Common Ratio
  3. Common Difference
  4. Sum up to 'n' Terms
  5. AP Puzzle
  6. GP Logical Puzzle
With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. Reinforce these ideas with these questions.